In a wide variety of manufacturing and quality assurance applications it is necessary to precisely locate the center of a surface feature of an object in order to position the object or to carry out various measurements such as measurements of effective size, out-of-roundness, runout and/or eccentricity. The methods and equipment used to measure vehicle wheels and their components are good examples of such applications.
By way of background, wheels are normally manufactured from two components: a central disk or "spider" which is press fitted and welded inside a tire-supporting rim. The rim and disk each possess a number of significant surface features which, in order to produce a satisfactory wheel, must be properly shaped and/or maintained in a desired positional relationship with other surface features of the same component or, in the case of an assembled wheel, positioned correctly with respect to certain surface features of its mating component.
For instance, the disk usually contains a central pilot hole adapted to receive the center flange of a vehicle hub. The pilot is usually surrounded by a so-called "bolt circle" which comprises an array of four or five mutually spaced smaller holes ringing the pilot hole. The holes in the bolt circle receive lug bolts for effectively securing the disk to the hub. The bolt circle must be maintained concentric with the pilot hole within controlled tolerances. Also, the profile of the pilot hole must be suitably round and of a proper effective size to ensure it will fit onto the vehicle hub correctly. As used herein, the "effective size" of a circular feature refers to the size of the mating feature of perfect roundness that will fit the feature with zero clearance. Plug and ring gauges are familiar examples of precision made mechanical devices which can be used to measure the effective size of inside and outside dimensions, respectively. The rim component of a wheel also includes a number of surface features of significance including pairs of opposed bead seats and safety humps, respectively, each of which must be of a proper diameter and properly centered with respect to one another on the rim. When the wheel is assembled, it is important that bead seats on the rim also be centered properly with respect to the pilot and/or bolt circle on the disk.
To carry out these and other measurements, machines for measuring wheels or wheel components have generally relied on the use of precision mechanical fixturing devices to mechanically locate the center of a surface feature of the component or assembly to be measured by means of engagement with that surface feature to physically align the surface feature with a known center axis associated with the fixture. For example, it has been known to mechanically center a wheel or component to be measured by mounting it on a precision fixture known to be perfectly round and of an exactly known size, with the center axis of the fixture serving as a measuring reference axis. Provided the fixture is sized to tangentially engage the pilot hole or other surface feature (at at least two points in the case of an elliptical profile and at least three points otherwise) such a fixture serves to mechanically center the surface feature on the fixture even though the profile of the feature may not be truly round as it should be. The effective size of the surface feature is equal to the diameter of the engaging portion of the fixture which effectively functions as either a plug gauge or ring gauge depending on whether the fixture engages the surface feature from the inside or outside, respectively.
However, precision mechanical fixtures of this type are subject to wear which degrades the accuracy of measurements made using them. Also, in the event of changes in the size and/or shape of the surface feature due to manufacturing variations, a differently sized fixture would be required thereby necessitating changeover delays as well as the expense of fabricating fixtures of different sizes. In attempt to overcome the difficulties associated with precision mechanical fixtures, adjustable mechanical centering devices such as expandable collets have also been known. While eliminating the need for fixtures of different sizes, adjustable devices of this type are even more expensive to fabricate and are also subject to wear.
It has also been known to gauge the size of a profile of a surface feature of an object by arranging electromechanical distance or angle transducers to respond to degree to which an expandable collet must open to properly engage the surface feature. However, such equipment is also expensive to fabricate with good precision and is subject to degraded performance through mechanical wear. Moreover, measurements made this way are not always satisfactory since the size and shape of the collet may prevent it from engaging an imperfectly circular surface feature at locations which accurately reflect the effective size of the surface feature or its true center.
The American National Standard for Measurement of Out-Of-Roundness, ANSI B89.3.1-1972, describes a number of techniques for determining the center of a profile including the Minimum Radial Separations (MRS), Least Squares Circle (LSC), Maximum Inscribed Circle (MIC), and Minimum Circumscribed Circle (MCC) methods. The standard recognizes that determination of the Maximum Inscribed Circle (MIC) associated with a polar profile is useful when it is desired to read the out-of-roundness of a polar profile in terms of the radial deviations from the interior of the profile to the perimeter of the largest ideally round plug gauge which can be fitted to it (i.e. the radial deviation between the actual profile and the circle defining its effective size). The standard further recognizes that the MIC and MCC techniques are both useful constructs for centering an arc.
Unfortunately, neither ANSI B89.3.1-1972 nor any other prior art Applicants are currently aware of describes a way of accurately and rapidly determining the maximum inscribed circle (MIC) of a surface feature in a manner which does not rely on trial and error and which is readily adaptable to the construction of automated or semiautomated measuring machines which do not rely on a human operator to determine measurement values. For instance, the above ANSI standard proposes finding the maximum inscribed circle "graphically by trial and error with the aid of a bow compass or engraved circles on a transparent template". Further according to that standard, to "determine the out-of-roundness value from meter or indicator readings alone the part must be centered to produce either two or three equal minimum readings depending on the profile shape. If the overall figure is 2-lobed, i.e. oval or elliptical, proper centering will produce two minimum readings spaced at 180 degrees. All other figures should be centered to produce at least three equal minimum readings spaced over more than 180 degrees." ANSI B89.3.1-1972 at page 11 (emphasis added). However, the standard provides no guidance on how such centering could be carried out by a machine and without the use of trial and error.